Model reconstruction from temporal data for coupled oscillator networks

In a complex system, the interactions between individual agents often lead to emergent collective behavior like spontaneous synchronization, swarming, and pattern formation. The topology of the network of interactions can have a dramatic influence over those dynamics. In many studies, researchers start with a specific model for both the intrinsic dynamics of each agent and the interaction network, and attempt to learn about the dynamics that can be observed in the model. Here we consider the inverse problem: given the dynamics of a system, can one learn about the underlying network? We investigate arbitrary networks of coupled phase-oscillators whose dynamics are characterized by synchronization. We demonstrate that, given sufficient observational data on the transient evolution of each oscillator, one can use machine learning methods to reconstruct the interaction network and simultaneously identify the parameters of a model for the intrinsic dynamics of the oscillators and their coupling. Keywords: nonlinear dynamics, phase oscillators, Kuramoto oscillators, network reconstruction, network topology, machine learning, computational methods 1. Introduction Nature and society brim with systems of coupled oscillators, including pacemaker cells in the heart, insulin-secreting cells in the pancreas, neural networks in the brain, fireflies that synchronize their flashing, chemical reactions, Josephson junctions, power grids, metronomes, and applause in human crowds, to name merely a few [1-9]. The dynamics of coupled oscillators in complex networks have been studied extensively.